Sand Hill-bert Curve

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Although I’ve never managed to make a particularly castle-y sand castle, I’ve always loved making sand castles at the beach. The last couple of times that I’ve been to a sandy beach, I’ve been particularly inspired by the idea of creating fractal sand castles. Something about a fractal sand castle on a fractal coastline just feels right.

Long time readers of my blog might remember the Sand-pinski Triangle that I created on a previous trip to the beach.

On my most recent beach trip, I hilled up some more sand to create a Sand Hill-bert curve. The Hilbert Curve is a fractal space filling curve discovered by David Hilbert. It’s shown up in line-enveloped form in my blog before. The Sand Hill-bert Curve is a third order Hilbert Curve, although I’ve taken the liberty of adding some ellipsis so that you know that it could keep going and filling all of space.

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Although you can get a pretty good sense of the 3-dimensionality of the sand hill from the shadows in the picture, I love the effect created by this awesome 3D rendered animated GIF that Emily Eifler made for me. Also, there is something delightfully weird about the idea that the sand castle might be hollow.

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The International Congress of Mathematicians

If you are involved in the mathematics community, you’ve probably heard of the International Congress of Mathematicians. In addition to being the largest gathering of professional mathematicians in the world, it’s also the place where the Fields Medals, often considered to be the greatest prize in mathematics, are awarded by the International Mathematical Union.

The ICM, like 6OSME, is held only once every 4 years. This year, it was held in Seoul at the same time as the Bridges Math Art Conference (the subject of my last post), for reasons that were, of course, entirely non-accidental.

As a fairly active participant in Bridges, I didn’t spend as much time at the ICM as it deserved, but I did make it there for a few talks.